1. Chapter 5
Risk and Return

2. After studying Chapter 5, you should be able to:
Understand the meaning of risk, return and risk preferences.
Measure the risk and return of a single asset.
Measure the risk and return of a portfolio of assets.
Explain beta and the CAPM model.
Analyse shifts in the securities market line.

3. Defining Return R = Dt + (Pt – Pt - 1 ) Pt - 1
Return is defined as “the total gain or loss experienced on an investment over a given period of time”.
Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. (see eqn 5.1 p.98)
It is measured as follows:
Dt + (Pt – Pt - 1 )
R =
Pt - 1

4. Defining Return Where:
R = Actual, expected or required rate of return during the period t
Dt = Cash flow received from the investment in the time period [t – 1 to t]
Pt = Price of the asset at time t
Pt-1 = Price of the asset at time t – 1

5. Return Example = 5% R = $1.00 + ($9.50 – $10.00 ) $10.00
The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend.
What return was earned over the past year?
$ ($9.50 – $10.00 )
= 5%
R =
$10.00

6. Another Example

7. Defining Risk
Risk is defined as “the chance of financial loss”. It is the variability (difference) of returns from those that are expected.
What rate of return do you expect on your investment (savings) this year?
What rate will you actually earn?
Does it matter if it is a bank deposit or a share of stock?

8. The Risk-Return Trade-off
Investments must be analysed in terms of both their return potential and their riskiness or variability.
Historically, its been shown that higher returns are accompanied by higher risks.

9. Risk Preferences Three Preferences:
Risk Averse: Require a higher rate of return to compensate for taking higher risk.
Risk Seeking: Will accept a lower return for a greater risk.
Risk Indifferent: Required return does not change in response to a change in risk.

10. Risk Preferences

11. Risk Assessment Of A Single Asset – Probability Distribution
Provides a more quantitative, yet behavioural, insight into an asset’s risk.
Probability is the chance of a particular outcome occurring.
Can be graphed as a model relating probabilities and their associated outcomes.
The expected value of a return R [the most likely return on an asset] can be calculated by:

12. Determining Expected Return (Discrete Dist.)
R = S ( Ri )( Pi )
R is the expected return for the asset,
Ri is the return for the ith possibility,
Pi is the probability of that return occurring,
n is the total number of possibilities.
I = 1

13. Probability Distribution
A probability distribution is a model that relates probabilities to the associated outcomes.
The simplest type of probability distribution is the bar chart, which shows only a limited number of outcome-probability coordinates.

14. How to Determine the Expected Return
Stock BW
Ri Pi (Ri)(Pi)
–0.015
–0.006
Sum
The expected return, R, for Stock BW is .09 or 9%

15. Probability Distribution
The bar charts for Shuia Na Ltd’s assets A and B are shown in Slide 15.
Although both assets have the same most likely return, the range of return is much more dispersed for asset B than for asset A—16% versus 4%.

16. Probability Distribution

17. Probability Distribution
If we knew all the possible outcomes and associated probabilities, a continuous probability distribution could be developed. This type of distribution can be thought of as a bar chart for a very large number of outcomes.
Slide 17 shows continuous probability distributions for assets A and B. Note that although assets A and B have the same most likely return (15%), the distribution of returns for asset B has much greater dispersion than the distribution for asset A.
Clearly, asset B is more risky than asset A.

18. Probability Distribution

19. Discrete versus Continuous Distributions
Discrete Continuous

20. Risk Measurement – Standard Deviation
A normal probability distribution will always resemble a bell shaped curve.

21. Risk Measurement – Standard Deviation
Measures the dispersion around the expected value.
The higher the standard deviation the higher the risk.

22. Determining Standard Deviation (Risk Measure)
s = S ( Ri – R )2( Pi )
Standard Deviation, s, is a statistical measure of the variability of a distribution around its mean.
It is the square root of variance.
Note, this is for a discrete distribution.
i = 1

23. How to Determine the Expected Return and Standard Deviation
Stock BW
Ri Pi (Ri)(Pi) (Ri - R )2(Pi)
– –
– –
Sum

24. Determining Standard Deviation (Risk Measure)
s = S ( Ri – R )2( Pi )
s =
s = or 13.15%
i=1

25. Another example
Shuia Na Ltd, a tennis-equipment manufacturer, is attempting to choose the better of two alternative investments, A and B. Each requires an initial outlay of $10,000 and each has a most likely annual rate of return of 15%. To evaluate the riskiness of these assets, management has made pessimistic (worse case) and optimistic (best case) estimates of the returns associated with each.
The expected values for these assets are presented in the Table on slide 26. Column 1 gives the Pri’s and column 2 gives the ri’s, n equals 3 in each case. The expected value for each asset’s return is 15%.
Slide 27 shows the standard deviations for these assets

26. Another example – cont.
Before looking at the standard deviations, can you identify which asset is most risky?

27. Another example – cont.

28. Which Asset Is Riskier?

29. Risk Measurement – Coefficient Of Variation
A measure of relative dispersion, useful in comparing the risk of assets that have different expected returns.
The higher the coefficient of variation, the greater the risk.
Allows comparison of assets that have different expected returns.

30. Coefficient of Variation
The ratio of the standard deviation of a distribution to the mean (average) of that distribution.
It is a measure of RELATIVE risk.
CV = s/R
CV of BW = / 0.09 = 1.46

31. Risk Attitudes
Certainty Equivalent (CE) is the amount of cash someone would require with certainty at a point in time to make that person indifferent between that certain amount and an amount expected to be received with risk at the same point in time.

32. Risk Attitudes Certainty equivalent > Expected value
Risk Preference
Certainty equivalent = Expected value
Risk Indifference
Certainty equivalent < Expected value
Risk Aversion
Most individuals are Risk Averse.

33. Risk Attitude Example
You have the choice between (1) a guaranteed dollar reward or (2) a coin-flip gamble of $100,000 (50% chance) or $0 (50% chance). The expected value of the gamble is $50,000.
Mary requires a guaranteed $25,000, or more, to call off the gamble.
Raleigh is just as happy to take $50,000 or take the risky gamble.
Shannon requires at least $52,000 to call off the gamble.

34. What are the Risk Attitude tendencies of each?
Risk Attitude Example
What are the Risk Attitude tendencies of each?
Mary shows “risk aversion” because her “certainty equivalent” < the expected value of the gamble.
Raleigh exhibits “risk indifference” because her “certainty equivalent” equals the expected value of the gamble.
Shannon reveals a “risk preference” because her “certainty equivalent” > the expected value of the gamble.

35. Portfolios A portfolio is a collection of assets.
An efficient portfolio is:
One that maximises the return for a given level of risk. OR
One that minimises risk for a given level of return.

36. Portfolio Return
Is calculated as a weighted average of returns on the individual assets from which it is formed.
Is calculated by (Eqn 5.6):

37. Determining Portfolio Expected Return
RP = S ( Wj )( Rj )
RP is the expected return for the portfolio,
Wj is the weight (investment proportion) for the jth asset in the portfolio,
Rj is the expected return of the jth asset,
m is the total number of assets in the portfolio.
J = 1

38. Correlation
A statistical measure of the relationship, if any, between a series of numbers representing data of any kind.
Three types:
Positive Correlation: Two series move in the same direction.
Uncorrelated: No relationship between the two series.
Negative Correlation: Two series move in opposite directions.

39. Correlation Coefficient
A standardised statistical measure of the linear relationship between two variables.
Its range is from –1.0 (perfect negative correlation), through 0 (no correlation), to +1.0 (perfect positive correlation).

40. Correlation
The degree of correlation is measured by the correlation coefficient.

41. Diversification
Combining assets with low or negative correlation can reduce the overall risk of the portfolio.
Combining uncorrelated risks can reduce overall portfolio risk.
Combining two perfectly positively correlated assets cannot reduce the risk below the risk of the least risky asset.
Combining two assets with less than perfectly positive correlations can reduce the total risk to a level below that of either asset.

42. Diversification

43. Correlation, Diversification, Risk & Return
The lower the correlation between asset returns, the greater the potential diversification of risk.

44. What is the expected return and standard deviation of the portfolio?
Portfolio Risk and Expected Return Example
You are creating a portfolio of Stock D and Stock BW (from earlier). You are investing $2,000 in Stock BW and $3,000 in Stock D. Remember that Stock BW’s the expected return is 9% and its standard deviation is13.15%. Stock D’s expected return is 8% and its standard deviation is 10.65%. The correlation coefficient between BW and D is 0.75.
What is the expected return and standard deviation of the portfolio?

45. RP = (WBW)(RBW) + (WD)(RD)
Determining Portfolio Expected Return
WBW = $2,000/$5,000 = 0.4
WD = $3,000/$5,000 = 0.6
RP = (WBW)(RBW) + (WD)(RD)
RP = (0.4)(9%) + (0.6)(8%)
RP = (3.6%) + (4.8%) = 8.4%

46. You will not be asked to do this calculation.
Determining Portfolio Standard Deviation
sP = (2)(0.0025)
sP = SQRT(0.0119)
sP = or 10.91%
You will not be asked to do this calculation.

47. The WRONG way to calculate is a weighted average like:
Determining Portfolio Standard Deviation
The WRONG way to calculate is a weighted average like:
sP = 0.4 (13.15%) + 0.6(10.65%)
sP = = 11.65%
10.91% = 11.65%
This is INCORRECT.

48. Summary of the Portfolio Return and Risk Calculation
Stock C Stock D Portfolio
Return % % %
Stand.
Dev % % % CV
The portfolio has the LOWEST coefficient of variation due to diversification.

49. Diversification and the Correlation Coefficient
Combination
E and F
SECURITY E
SECURITY F
INVESTMENT RETURN
TIME
TIME
TIME
Combining securities that are not perfectly, positively correlated reduces risk.

50. Total Risk = Systematic Risk + Unsystematic Risk
Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. It cannot be avoided
Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification.

51. Systematic Risk and Unsystematic Risk
Other names for these terms are:
Systematic risk
Unavoidable risk
Nondiversifiable risk
Unsystematic risk
Avoidable risk
Diversifiable risk

52. Unsystematic (diversifiable) risk Systematic (nondiversifiable) risk
Total Risk = Systematic Risk + Unsystematic Risk
Factors such as changes in the nation’s
economy, tax reform by the Congress,
or a change in the world situation.
STD DEV OF PORTFOLIO RETURN
Unsystematic (diversifiable) risk
Total
Risk
Systematic (nondiversifiable) risk
NUMBER OF SECURITIES IN THE PORTFOLIO

53. Total Risk = Systematic Risk + Unsystematic Risk
Factors unique to a particular company
or industry. For example, the death of a
key executive or loss of a governmental
defense contract.
STD DEV OF PORTFOLIO RETURN
Unsystematic risk
Total
Risk
Systematic risk
NUMBER OF SECURITIES IN THE PORTFOLIO

54. Capital Asset Pricing Model (CAPM)
CAPM is a model that describes the relationship between risk and expected (required) return.
In this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security.

55. CAPM Assumptions 1. Capital markets are efficient.
2. Homogeneous investor expectations over a given period – i.e all investors have similar expectations
3. Risk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy).
4. Market portfolio contains only systematic risk (use S&P 500 Index or similar as a proxy).

56. Characteristic Line
This is a line that describes the relationship between an individual security’s returns and returns on the market portfolio.
The slope of this line is called Beta

57. Characteristic Line Beta = Characteristic Line EXCESS RETURN ON STOCK
Narrower spread
is higher correlation
Rise
Run
Beta =
EXCESS RETURN
ON MARKET PORTFOLIO
Characteristic Line

58. What is Beta? An index of systematic risk.
It is the measure of market (non-diversifiable) risk, and measures the sensitivity of a stock’s returns to changes in returns on the market portfolio.
The beta for the market portfolio is 1.0
The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio.

59. Characteristic Lines and Different Betas
(aggressive)
EXCESS RETURN
ON STOCK
Beta = 1
Each characteristic
line has a
different slope.
Beta < 1
(defensive)
EXCESS RETURN
ON MARKET PORTFOLIO

60. Security Market Line Rj = Rf + bj(RM – Rf)
Rj is the required rate of return for stock j,
Rf is the risk-free rate of return,
bj is the beta of stock j (measures systematic risk of stock j),
RM is the expected return for the market portfolio.
This is also known as the CAPM formula

61. Systematic Risk (Beta)
Security Market Line
Rj = Rf + bj(RM – Rf)
Risk
Premium RM
Required Return Rf
Risk-free
Return
bM = 1.0
Systematic Risk (Beta)

62. Capital Asset Pricing Model (CAPM) – Beta Coefficient

63. Capital Asset Pricing Model (CAPM) – Portfolio Betas
Are interpreted exactly the same way as individual asset betas.
Can calculated by:
Where:
wj = The proportion of the portfolio’s dollar value represented by asset j
βj = The beta of asset j

64. Determination of the Required Rate of Return
Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a 6% Rf and a long-term market expected rate of return of 10%. A stock analyst following the firm has calculated that the firm beta is What is the required rate of return on the stock of Basket Wonders?

65. BWs Required Rate of Return
RBW = Rf + bj(RM – Rf)
RBW = 6% + 1.2(10% – 6%)
RBW = 10.8%
The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0).

66. Determination of the Intrinsic Value of BW
Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling for $15.
What is the intrinsic value of the stock? Is the stock over or underpriced?

67. Remember, from Chapter 4, the value of a share of stock is calculated by:
V = D1/(ke – g)
So the intrinsic value of BW is:

68. Determination of the Intrinsic Value of BW
$0.50
Intrinsic
Value =
10.8% – 5.8% =
$10
The stock is OVERVALUED as the market price ($15) exceeds the intrinsic value ($10).

69. Systematic Risk (Beta)
Security Market Line
Stock X (Underpriced)
Direction of
Movement
Direction of
Movement
Required Return Rf
Stock Y (Overpriced)
Systematic Risk (Beta)